{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 检查较小的两个图是否同构\n",
    "\n",
    "import igraph as ig\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 生成三个不同的图\n",
    "g1 = ig.Graph([(0, 1), (0, 2), (0, 4), (1, 2), (1, 3), (2, 3), (2, 4), (3, 4)])\n",
    "g2 = ig.Graph([(4, 2), (4, 3), (4, 0), (2, 3), (2, 1), (3, 1), (3, 0), (1, 0)])\n",
    "g3 = ig.Graph([(4, 1), (4, 3), (4, 0), (2, 3), (2, 1), (3, 1), (3, 0), (1, 0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Are the graphs g1 and g2 isomorphic?\n",
      "True\n",
      "Are the graphs g1 and g3 isomorphic?\n",
      "False\n",
      "Are the graphs g2 and g3 isomorphic?\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "# 检查它们是否同构\n",
    "print(\"Are the graphs g1 and g2 isomorphic?\")\n",
    "print(g1.isomorphic(g2))\n",
    "print(\"Are the graphs g1 and g3 isomorphic?\")\n",
    "print(g1.isomorphic(g3))\n",
    "print(\"Are the graphs g2 and g3 isomorphic?\")\n",
    "print(g2.isomorphic(g3))\n",
    "\n",
    "# Output:\n",
    "# Are the graphs g1 and g2 isomorphic?\n",
    "# True\n",
    "# Are the graphs g1 and g3 isomorphic?\n",
    "# False\n",
    "# Are the graphs g2 and g3 isomorphic?\n",
    "# False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAACsCAYAAADmDq9FAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/P9b71AAAACXBIWXMAAA9hAAAPYQGoP6dpAAB3LUlEQVR4nO2ddVxUaRfHv4SB3a1gd1Aqyti5q6uurWsHYCEGKtZaKHYLdnd3rTWIBYoIiF2sLShICMzc9w9e7ooMSMwwg9zv5+MfM/e5zz0zHp45T5zf0RMEQUBCQkJCQkIi06KvbQMkJCQkJCQktIsUDEhISEhISGRypGBAQkJCQkIikyMFAxISEhISEpkcKRiQkJCQkJDI5EjBgISEhISERCZHCgYkJCQkJCQyOVIwICEhISEhkcmRggEJCQkJCYlMjhQMSEhISEhIZHKkYEBCQkJCQiKTIwUDEhISEhISmRwpGJCQkJCQkMjkSMGAhISEhIREJkcKBiQkJCQkJDI5hto2IDPx/v17Tp48iaenJ3fv+hASGoqhoSFlSpfCwsKChg0b0qhRI/T1pRhNQrcICgrixIkTeHp64n33Lp8/f8HAwICSJUtgaWFBgwYNaNq0KQYGBto2VUIiHl++fBF99463N8HBn9HX16d48WJYmJtTv359WrZsiaFh5v451BMEQdC2Eb86Pj4+uLi4sG/fPmJiYihVrgJlKlclV978KGJiePfqBc/87/E15AvlK1RgxPDhDBs2jKxZs2rbdIlMzoMHD5g3bx67d+8mMjKSkiblKFOlOnnyF0CpUPD+35c887tHyOdgyhgbM8zOjlGjRmFkZKRt0yUyOc+ePcPFxYVt27cTHhZG8TLGGFepQZ4CBRGUSj6++Zdn/vf4/OkjJUqWxGboUBwcHMidO7e2TdcKUjCgQaKjo3F2dmb27NkUKl6S1r3607RjV3LnL5CgrSAIBNy+yZmdW/A4c5yqVaqyZctmzMzMtGC5RGZHoVCwePFipk6dSp4ChWjVoy/NOvcgX6HCCdoKgsDje96c2bUF9xOHMTE2YcuWzVhZWWnBconMjlKpZM2aNThOmED2HDlp2b0Pzbv2omDR4gnaCoLA8wA/zuzaypWjByhatAibNm6kWbNmWrBcu0jBgIYIDQ3ljw4dkF+5QiebkXSxHU2WZM70n933ZdUkBwKfPGTHjh107dpVw9ZKSPxHREQEXbt24+TJE7TrN5Seox3Jlj15M/3AJ49Y5eTA43verFu3joEDB2rYWgmJ/4iOjqZP377s2b2bVj360nfcFIxy5UrWvW9fvWD15DH43bzG0qVLsbe317C1uoUUDGiAyMhIWrdpg9ft20xcs5VqFvVS3Ed0VBSrJ4/B/cRhDhw4QMeOHdVvqITED8TExNChQ0f+uXCB8SvWYyprmuI+FAoF62dN5uzurWzdupU+ffpowFIJifgolUp69urFwYMHGb1gFVZt2qWqjx2LnTm8fjWrVq1i2LBhGrBUN5GCAQ3g6OjI0mXL+HvzXqqY1Y13LSIsjCMbVvPI5w6P73nz9ctnhjsvodmf3RP0o1AoWOxgi991OX6+vpQuXTq9PoJEJmXOnDlMmzaNyWu3U8e6SbxrKfFdQRBY5eTAtVNH8fb2pnLlyun0CSQyKytXrmTkyJGMW7YOq9a/x7uWUt/dNHc6Z3Zu5ubNm5iamqbXR9Aq0rF1NXP9+nUWLVpEtxFjEwQCAKHBQexbvYTAp48wrlwtyb4MDAwYNnsh2XLkZPDgIUhxm4Qm8fX1ZcaMGXQYNCxBIAAp8109PT2GTHOmQNHi9O8/AIVCoSGrJSTg6dOnTJgwgdY9+yUIBCDlvttn3BRKV6hMv379iYqK0pTZOoUUDKiZ6dP/xrhSVToMtFN5PX+RIqyXe+N24RZ9x0/9aX858+Rl0NQ5nD17hqtXr6rbXAkJkVmzZlGoeEm6jRij8npKfTebUQ5sZi7g+vVrnD59Wt3mSkiIzJs3j+y5ctNn3BSV11Pqu1myZmXYnEXcu+fD/v371W2uTiIFA2rk8ePHnD17ht/7DcEgkZzVLFmzkb9wkRT1a9G0FSVMyrF69Wp1mCkhkYA3b95w8OBB2v41kKzZsqtskxrfrV7Xigo1arFqleS7Eprh8+fPbN+xg1Y9+mKUM6fKNqnx3XLVa1GzvnWm8V0pGFAje/fuJUeuXDRo216t/err69O8S08OHDiQaZasJNKXgwcPgp4eTTqqN3NFT0+P5l16c/r0KT5//qzWviUkAI4fP05EeDjNO/dUe98tuvbCw+Mqr169UnvfuoYUDKgRT09Pyteok+w0rJRQ1bweUVFR+Pr6qr1vCQlPT09MKlclZ568au+7qkU9BEHgzp07au9bQsLT05MSxmUpULSY2vuu+v9MMC8vL7X3rWtIwYAauX3Hm7LVamikb5Mq1dDX15cGVAmNcPuONyZVa2qk7xJly5PdKIfkuxIa4Y63NyYaGncLFClGvkKFM4XvSsGAGvny5TN5VKgLqoNsRjkwyplTWmqV0AifP2vOdw0MDMidP7/kuxIaIThYc76rp6dHvgIFM4XvSsGAGtHT09No+p9SoZSKGEloBM37rkLyXQmNEOu7mutfqcwc4+6v/wnTkWJFi/HxzWuN9B0aHEREeBhFixbVSP8SmZvixYrx8c2/Guk76lsknz99lHxXQiMUL1aMj68147tKpZKPb19nCt/N3DUb1URMTAx3794lRw4jHvtoZm/pqf89AMzNzTXSv0TmRKFQ4OvrS5Yshhrz3RcP7qOIiZF8V0KtKJVK/P390dODx/c047tvnj8l/OvXTOG7UjCQSqKiorhz5w5yuRwPDw9CQ0P5+vUrzx8/4UvQJ/IWKJjovSe3byQ8NISg9+8A8Lx4jqB3bwBo+9dAcubOk+Ceux5XyJc/PxUrVtTMB5LINMTExODt7S367ufPnwkKCuLNy+e8D3xFkVKJy16n1nezZ89OrVq1NPOBJDINCoUCHx8f5HI5V69eJSgoiA8fPvAl6BMvHtzHuHLVRO9Nre8aGBhkimBAqk2QAiIjI7l16xbu7u5cv36d8PDweNejoqK4evUqPUdPoNOQEYn2Y9usLh9eB6q8tub8jQSDcdS3SGyaWDCofz8WL16c9g8ikemIiorCy8sLuVzO9evXCQ0NjXddoVDgfvUq7fvb0HvMpET7SanvKhQKhreoT7s2rdi4cWPaP4hEpiM6Ojpe8Prly5d415VKJR7XrtGkUzeGTJubaD8p9V1BEBjTvikWtWtyIBOoEEorAz8hPDycGzduIJfLuXXrFpGRkQnaGBkZUa9ePWQyGWvXruXktg206t4n0Zxt1ws3U2TDmV1bCQkOwtbWNlWfQSJzEhERgaenJ3K5nBs3biQIXgGyZctG3bp1sba2Zv/+/WzfuY3f+w4mX6HCKvtMqe9eOryXD2/+Zfjw4an6DBKZk6ioKNF3r1+/ztevXxO0yZIlCxYWFshkMs6fP8/yFSvpMHBYoitbKfXd62dP8vLxQza5rUnVZ8hoSCsDKggNDeX69etcuXIFLy8voqOjE7TJlSsXVlZWWFtbY2FhQdasWQF49eoV1WvUwKJ5G0bMXZpmW14/f8q4ji0ZOmQwy5cvT3N/Er82YWFh8YLXb9++JWiTI0cOMXi1sLDAyChWJOvDhw9Uq16d8nUsGL98PXp6emmy5dO7Nzi0a0rnTh3ZsmVLmvqS+PWJiIjg5s2buLu7c+PGDSIiIhK0yZ49O5aWlshkMurVq0eOHDkACAkJoXqNGhQoZcK0jbvT7LshwZ9waNeURtYNOXzoUJr7ywhIwcD/+fz5Mx4eHsjlcu7cuaOyylrevHlp0KABMpmMOnXqkCVLFpV9bdiwgcGDBzP073m07tE31TZ9/fKZ6X07oxf9jXs+PuRMRHdbInMTEhLCtWvXcHd3TzR4zZ07N1ZWVshkMszMzMTg9Uf2799P165d+WusU5JbXT8jIiyMmQO7E/L+Df5+fuTPnz/VfUn8uoSFhXH9+nUxeFUlt54jR454E6/s2VXXzjh79iytW7fmz6Ejk9zq+hlR3yJxtulL4EN//P38KFZM/cqGuki6bxMIgqAzUdbHjx+5evUqcrmce/fuoVQqE7QpUKAA1tbWyGQyatasiYGBwU/7HThwID4+Piz/eyLfwsNpP8AmxZ/5w+tA5tr2I/TTe+RXrkiBgA6gS74bHBws+u7du3dVBq/58uWjYcOGWFtbU6dOHQwTKZ71PV26dGHq1KnMmjWLqMhIugxzSJbPx7Ptw3vmjxjI66ePuHTxohQI6AC65LshISHxJl6JBa9xEy9TU9NEg9fvadWqFQsXLmTcuHFER0Xx11gnDBOZsCVGaHAQC0fb8OiuF2fPnMk0gQBoeGVAoVBw6tQpjh8/jqenF/7+fkRERGBoaIhJ2XJYWpjTpEkTevbsSe7cuTVlRjzevXuHXC5HLpfj7++vsk2RIkWQyWTIZDKqVq2aKsGJkJAQ6tevz/3796lRryHD5iyiaKkyP71PoVBw4cBuNs+djp4ezJo5k7Fjx6b4+RJpQ6lUcv78eY4cOYKnpxe+fr6Eh4VhaGhI6TLGWFqYI5PJ6N27d7r92H38+BF3d3fkcjm+vr4qg9eCBQsik8mwtramRo0aKf4hh9hzMtbW1ty5402l2qaMmLuUkuUq/PQ+QRCQHz/EupmTUERH4zh+PDNnzkzx8yXShiAIXL58mYMHD+Lp6YXPPR/Cvn7FwMCAkqVKY2lhTsOGDenTpw+FChVKF5uCgoK4evUq7u7ueHt7q/Td/Pnz07BhQ2QyGbVq1UpW8PojUVFRNG3alGvXrmFcuRojXZZhUrnaT+8TBIEb507hOn0838LCsLOzY+nSpSl+fkZGI8GAUqlkzZo1zF+wgJcvXlCqXAUq1DTFuEo1jHLmIiY6itfPnvDUz4eHd29jlCMHgwYOZMaMGeTLl0/d5hAYGIi7uztXrlzh0aNHKtuULFlSHEQrVaqUpihaEARmzZqFXC7n06dPPHnylLCwr1g2a02zzj2oVMec3Pn++wFRKBS8fvYEr0vnOLdnG29fvaREyZJUqliRbNmysWzZMipXrpxqeySSjyAIbNq0Cee5c3ny+DHFy5hQsbYZJlWqkyN3HhQx0bx58Yynvnd5cPc2WbNkoU+fPsyZM0cjA+ubN2/EAOD+/fsq2xQrVkxcvapSpUqa1dIWLVrE6dOnCQ4O5vGTJ4R8+YJ5k+Y079KLyqaW8dJmlUolb54/5Y78Imd3b+XfZ08oVry46Lvz58+nTp06abJHInkIgsDu3buZNXs29/39KVqqNBVqmVGuWg1y5smHQhHDu5fPxXFXD+jRowdz586lePHiarfn/fv3uLu74+7ujq+vr0qFy8KFC4sBQPXq1VMVvH6Pq6srBw4c4MuXLzx+/ITg4CDqWDemRZfeVDGvG6+MsSAIvH35nLtXL3N291ZePAygaNGiVKpUiWzZsjFjxgwaNGiQJnsyEmoPBp48eUL/AQNwl8tp9Ednfu8ziAo16yTa/tPb15zdu51T2zaQN08eNm7YQOvWrdNkgyAIPH/+XBxEnz17prKdiYkJ1tbWNGrUCBMTE7Uto508eZIlS5YAsctdixYt4tSpU6xctYr7/1+NKFKiFLny5kURE8P7fwOJCA8jW7ZsdO/eneHDh+Pr68uuXbsAKFGiBKtXr5a2CjRMYGAgAwcO4ty5szRo057f+w6isqllon4R/OE9/xzYxfHNa8meNQturq506tQpzXa8evUKuVyOu7t7osFrqVKlxNWrChUqqM13L126xJw5c4DYw1qLFy/m8uXLrFy5irt3vQEoXLwEufLmQ1Aqef86kPCvXzE0NKRLly4MGzaM169fs379eiB2pcLNzY28edVfDVHiP969e8dQGxuOHjmCRdOWtOs3lBr1GiTqFyHBn7hwcA/HN7khKGJYuWIFvXv3TrMdb968EVdeAwICVLYpXry4OPGqXLmy2qR+b968yeTJk4HYTIOFCxfi6enJqlWruXnzBgAFixQlR568KJVKgt69JSLsK/r6+vzRoQPDhw0jIiJCPKidO3du1q5dm26rJ9pGrcHA7du3adW6NVmMcjJszmKq17VK9r0f3/yL69TxeF+9jJubG0OGDEnRswVB4PHjx6IjBgaqzietWLGiOIsqXTpxcZXU8uLFC4YPHy6e4v77779p2LChaOPDhw/x8vLi3r17hIaGYmhoSKlSpTA3N8fc3Jw8eWKFL2JiYhgzZow4G2zevDkTJ05Uu70Ssdy/f5/mLVoQrQTbWQswlTVN9r3BH96zbsZEbpw/zcKFC1O8rRMXvF65cgV3d3eeP3+usl3ZsmXFQVSdwWscb968wdbWVkxBdHR0pGXLlqKNT58+xcvLi7t37/LlyxcMDAwoUaKE6Ltx2yVKpZJJkyZx+/ZtAOrXr8/MmTN1Zs/6V+PZs2c0a96czyGhDP3bhXot2yb73tDgIDbMmYr8+CGmTZvG33//neL/pxcvXogTrydPnqhsU7p0aTF4LV++vNp9ISgoCBsbG7Gg0PDhw+nYsaN4/fnz53h5eeHt7c2ePXuIjIwkX758LFiwAAsLCwoWjF3tEgSBmTNn4u7uDkDt2rVxcXFJ84pFRkBtwcCjR4+ob2VFwRKlmbxuR7xl8OSiVCrZMHsKp3duZteuXfTo0eOn7QMCAsRZ1Nu3b1W2q1q1qjiIamI5LI6oqChGjBghrkS0b9+eUaNGpbq/pAZnCfURGBhI3Xr1yJorD1M37I63lJhcBEFg55J5HFy7Ajc3N4YOHfrT9g8fPhQH0X//Va2tXrFiRRo1aoS1tTWlSpVKsV3JRVXwOWHChFQP2p8+fcLW1jbRwVlCPXz48IF69esTGaNk+ua9FC6ROh85uHYFOxbPZf78+YwfPz7JtnGBYdy4++LFC5XtypUrJwYAxsbGqbIrOaQ0+OzZsycfP36kUKFC4urr94SEhGBra8uHDx8A6N+/v1pWTXQdtQQDCoUCa2sZL9+8xXnP8QSBwON73lw8tBffmx58+PcVufPlp2Jtc3rZO1KibPl4bQVBYNn4Edy5fB4/X1/KlIl/6C5OSz1uL+rjx48J7NHX16dGjRrIZDIaNmxI4cKqBVTUzcqVKzly5AgQuwWxcuVKsmXLlqY+v1+2NTIyYvXq1Rr9UchsCIJAq1at8fb1Y96+kwkCgZT67toZk7hyeC/e3t4JznkolUru378vDqLv3r1TaVO1atXE4DW9TjNv2rSJnTt3ArHLuGvWrEnzttSNGzeYMmUKELtsu2LFCsqXL/+TuyRSQpeuXTl/4SLz9p2iSMn440JKfBdg26I5HNvoys2bNzEzM4t3TRAEHjx4IPru69eqC7JVrlxZXHktWbKk+j5oEuzdu5d169YBsdlfa9euTXJb6mfBAMC9e/cYN26cWLFw8eLFVK9eXSP26wpqCQaWLFnC2LFjmb3jEFXM6ia4vmDUEALu3KJB63YYV67K548fOLVjE5HhYczdfZwylarEax8WGsKY9s0wr12L06dPiYWA4vSoVdWW1tfXp06dOmIAkN7pTB4eHkyfPh2ArFmzsmrVKkxMTNTSd9yBLoidKS5btixRjQOJlLFx40YGDRrElHU7MZU1SXA9pb77LSKccZ1aUaZYUTw8rqJUKrl3757ou58+fUrwDH19fWrWrCn6bnrvUXp7e+Po6IggCBgYGLB06VKqVKny8xuTQdyBLohdKl61apUociSRNg4cOECXLl0Ys8SVhm3/SHA9pb4bEx3NpG6/k8NAjzt3bqOvr4+/v78YALx//z7BM/T09KhevboYvBYpkvJVtbTw4MED7O3tUSgU6Onp4eLigqmpaZL3JCcYANi2bRtbt24FoGjRori6upIrVy612q9LpDkYiI6OpnSZMtSUNcNu1kKVbQJu36J8jdpk+S5X9PXzp4z5ozlWrX/HfsHKBPd4nD7GotE2jBo1ilevXiXQUofY2Ya5uTnW1tZYWVmJ++3pzcePHxk6dKhoo729Pe3atVNb/xEREQwfPpxXr14B0LVr158uQ0v8HKVSSaXKlSlaoSpjl7qpbJMa3/V2v8Sswb0YNmwY79+/Vxm8GhgYYGpqikwmw8rKSmu5+F++fMHGxkYMUgYPHkz37t3V1n9UVBT29vY8fvwYgN9++w0HBwe19Z9ZEQQBMzNzyJWHqetV/6Clxncf3r3NpO7tGDx4MCEhIQQFBSVoo6+vT61atcTgNW6/Pb0JCwsTD6xC7I/8wIEDf3pfcoMBhULB+PHjuXcvtmJso0aNmDJlyi979iXNokOHDx/m3du3TPhrUKJtqphZJnivhEk5SleoROAT1ael67VoS/7CRdm/fz/Vqv2XJ5otW7Z4cpTaPmGvUCiYN2+eGAhYW1vz+++/q/UZRkZGODk5MWrUKKKjo9m3bx+mpqZYWib8XiWSz/nz53ny+DEDZ6oOYiF1vlu7YWOKG5dl/4ED1KpZU3w/LniNCwDSS1sjMQRBYOHChWIgYGZmRteuXdX6jKxZszJ58mTs7OyIjIzk5MmTmJmZ0bhxY7U+J7Nx8+ZNvL3v4OS2LdE2qfHdSrXNKF+jNocOHYo3wzY0NBSD1wYNGuhEdsiKFSvEQKBq1ar07Zt6tVdVGBgYMHHiRGxtbQkNDeXKlSucPn2atm2Tf0AzI5HmYODIkSOUr14rydKRqhAEgc+fPlK6QiWV1w0MDWnaqRsntq4je/bs1K9fn0aNGsXTUtcFdu/ezd27d4HYnFkHBweNRI4VKlRg8ODBrFkTWzRj/vz5rF27VlJ3SwNHjhyhhHFZKpumLKj6me/q6enRvEtPdi2bT9asWcU6AN9rqesCR44c4fr160CsWqGjo6Pa0ry+p1SpUowYMYKFC2ODriVLllClShWKFi2q9mdlFo4cOUK+goWoY90kRff9zHcBmnfpyboZk9DT0xNlgK2srHRqifzcuXP8888/QKxc8aRJk1IlUvQzihQpgoODgyietXr1aqpVq6bRA5HaIs1/+bc8vahYO+k9GlVcOXaQoHdvaPhbwr2uOCrWNuVbZCRLly5l8uTJyGQynQoE/Pz8xD0lfX19Jk2apNGtik6dOlGvXj0gtpbC/PnzVSp5SSQPT08vKtQyTXHwlizfrWWGIiaGmTNnMm3aNJo2bapTgcCTJ09Yu3at+HrcuHEaXe5t1aoVTZvGpmuGhYXh7OysUkJZInl4enpRoWadFKe8Jc93TREEgQkTJjBjxgxatmypU4FAYGAgK1asEF87ODhoNEtMJpOJ276RkZE4OzurrKGQ0UlTMBAVFcWjhw8wqVIjRfcFPn3E+plOVK5jTpOO3RJtF9fvw4cP02KmRvj69Stz584Vf4z/+usvan63JKwJ9PT0GDduHAUKFADA09NTPJwlkXL8/P0wqZKyE8LJ9d2yVWP7TUw0SJtEREQwZ84cURO+c+fOYpCpKfT09LC3txezI/z9/dm2LfElbomk8fPzw6SqZsbdMhWrYGBgIJ7z0CWio6NxdnYWKxq2adOGJk2aaPy5tra24oHwp0+fitkLvxJpCgYiIyMRBIEcKdj7DP7wHmebvuTInZtxy9YlGdnm/H+/qmpZaxNBEFiyZImYGlazZk169eqVLs/Oly9fvPzvjRs38uDBg3R59q+EIAiEff1KjtzJX8lJie/G9atrvguxJ/zjDqNWqFAhWYeu1EHOnDlxcnISv7edO3eKW2wSKeNr2FeMUjBbT4nvGmbJQjYjI5303U2bNokBdunSpRk2bFi6PDdbtmw4OTmJBZMOHz7MtWvX0uXZ6UWagoG4PRpFTEyy2oeFhjBnaG/CQkKYsm4nBYomnUMd8/9+dS2N7vTp01y5cgWAXLlyMXHixHRVqDIzMxNPfMfExODs7CwKE0kkDz09PQwNDVHEJKyYpooU++7/Z9265ruXL1/m5MmTQKzc8PcDXHpQtWpV+vfvD8QGZPPmzSMkJCTdnv+rYGhoiCJaM+OuIAjERMfonO/eunWLffv2AbF/V05OTum6bVy2bFlsbW3F1wsXLlSpc5NRSVMwYGRkRMFChXj9TLUE5fdEfYtkrl0/Xj9/ipPrliQPsMTx5vlTAJ06rPHixQtWr14tvh4zZky659YC9OvXT8wFf/36NStXJkwTkkia0mWMef1/H0uKVPnui1gVSl3y3Xfv3ok1MyBWFVATktw/o1u3buJJ9Y8fP7Jo0SKVRWwkEse4jDFvXmjGd4PevSHqW6RO+W5wcDDz588XXw8ePJgKFX5eSVPdtGvXTpSXDwkJwcXF5Zc5+5KmYEBPTw9zM3Oe+t1Lsp1CoWCxgy0Pvb0Yu3QtlU0tktX/E9+76BsYcPHiRW7fvq31Lz0qKgpnZ2ciIyMB+P3335HJZFqxxdDQECcnJ/FQ2rlz5zh//rxWbMmoWFqY88zPJ8k2afFd4KcCKOmFQqHA2dmZsLAwAJo0aZLmgmCpRV9fH0dHRzE9zcPDg2PHjmnFloyKhYU5z/w1M+4+/r/vmpubp9lOdaBUKpk/f76o11G3bl21FARLDXp6eowZM0ZUtfX29mbv3r1asUXdpDmboFEjGf63rhEWmvhS3xaXGdy6cBZTWVO+fvnM5aMH4v1LjJv/nCZv3rycOnWKCRMm0K1bNxYtWsSNGzfEw0/pybp163j69L/Viu+XjLRB8eLFsbe3F18vX748UZlQiYTIZDIe+twh+ENCZbU4Uuu7nhfOUqtWbZ3Ix4ZYNTX//1fMLFasGKNHj9aqeEqhQoXiaeC7uromWl1UIiEymYwXDwN4+/J5om3S4rvGxibpJif8Mw4cOICnpycQKzc8btw4rfpunjx5mDBhgpiGu3nzZvFvKyOTZgXC169fY2xsTL+Jf/PbX6oPIk3r0xm/W4kftjgQkPAHLPDpI+x/a0zt2rVV1hbIkSMHVlZWyGQyLCws0lwD4Gdcu3aNadOmAbH7VatWraJs2bIafWZyWbBgAWfPngVitcGXLFmic/t9ukhwcDAlS5ako80outjaq2yTGt/99PY1ds3rsXz58nQ74JQUd+/eZfz48QiCgL6+PkuWLIkn5KVNVq9ezaFDh4DYAHvlypVkz55dy1bpPuHh4ZQsVYrGf/ag7/ipKtukxndDPwcztLE5f0+fxqRJk9Rmb2p58OABo0ePJiYmBj09PebNm5egbkJKSa4C4c/YsmUL27dvB2IDbFdXV62L4KUFtdQm6NGzJ+cvXmLx0QvkypsvzUYJgsCCkYN47utNwP37Yl2CGzduiEv035M9e3bq1q0rCruo+1DJx48fsbGxEQ86jRw5kj/+SDxPN72JiIjAzs5OrHzXrVu3FJeAzqzY2Niwa+8+lhy7mKpqhapYMXE0ty+eIfDVK62rDIaEhGBjYyMedBo4cCA9e/bUqk3fExUVxahRo8TSt7///jujR4/WrlEZhAkTJrBi5SoWH71AkVLqOfuxYc5ULu7fyfPnz7VyFup7wsPDsbOzE1c7u3fvzuDBg9Pcr7qCAYVCwdixY/Hz8wNit96cnJwyrFyxWuTGFi5YQHRkBJvm/q2O7nA/fogb50+zetUq8uXLR+PGjZkyZQr79+9nxowZtGjRIl4EFhkZyZUrV5gzZw6dO3dm+vTpnDt3Ti2pMQqFAhcXFzEQaNCgAe3bt09zv+rEyMiIyZMni9kde/fuFZfVJJJmzpw5ZM+ahXUzJqrlEJvnxXNcOryXpUuWaD0QEASBRYsWiYFAnTp16NYt8fxybZA1a1acnJzE1YATJ04gl8u1bFXGYPLkyRQqVJDVU8aqRXzM7+Y1Tm7bgLOzs9YDAYitAhsXCFSpUkXMQtEVDAwMmDRpkijIdOnSJc6cOaNlq1KPWoKBUqVKsXzZMi4d3suhdWk71X7f6wau0xzp0bMnf/75Z7xr2bJlo0GDBkyYMIF9+/YxZ84c2rRpE0/1Lzo6Gg8PD+bPn0/Xrl1xcnLi5MmTfPnyJVX27N0bW44WYvc5x44dq5ORX8WKFeNFzfPnzyc4OFiLFmUMChUqhJurKzfOn2bnknlpCgie+vmw3HEkbdv+phMD17Fjx/Dw8AD+2+dMzxTY5FKmTBmGDx8uvl68eLHKCnkS8cmTJw8bN2zA98ZVNsyekibfDXzyiMUONljLZIwcOVKNVqaO8+fPc+7cOUCzcsNppWjRovEKb61atUrU8MhoqE2IvF+/fkydOpXti5zZMn8m0VHfUtzH1VNHmTmoJ3XrWrJxw4Yk22bJkoW6desyduxY9u7dy/z582nfvr2ozgexOfi3bt1iyZIldOvWjfHjx3P06FGVZWRV4e/vz+bNm4HYU6QTJ07UWmXE5NCpUyexeFFwcDALFiyQ5IqTQadOnVi4cCEH165g7YxJfItIuWaD16XzTOvbhSqVKrF79y6tB4zPnj3D1dVVfD1+/Ph0L42cElq3bi0qycWpe2o7eygj0KJFC9zc3Di9czMrJtoTkYrV0HvX3ZnW509KFCvK4UOHtB4wvn79muXLl4uv7e3tKVGihBYtSppGjRqJxekiIyOZM2dOhpQrVmtVkpkzZ7Jo0SJObdvAhC5t8bt1PVnR6vvAVyy0H8JiB1vy581L/379UrTvH1cOdtSoUezatYslS5bw559/xjt4qFQq8fb2ZsWKFfTs2ZPRo0dz8ODBRGcgYWFh8eSGe/XqRe3atZNtkzbQ19dn/PjxYvGiW7duiYezJJJm7NixuLm5ceXwXsZ1asXdq5eT5buf3r5mxUR7nG37kjOHEX379tF6wBg3IMVl3HTs2JH69etr1aaf8aNcsa+vLzt27NCyVRmDIUOGsH37dm6dP8WYDs25deFssiYBnz9+YO2MSfzdvxumtWtx5fJlrZUjjuNHueGWLVvSrFkzrdqUHGxtbSlTpgwQW/djw08ms7qIWg4Q/oiPjw/9+vfH+84dTKpUo/EfXahQyxSTKtUwypmLmOgo/n32hCe+d7lx7hS3L/9D3nz5KFO6NIULF8bAwEAtJ54FQeDhw4fI5XLkcnmiaXeVK1fG2toamUxGyZIlEQQBZ2dnLl26BEC1atVYvHix1iPm5OLl5cXEiROBWD2C5cuXU7FiRS1blTF48OAB/fsP4Pr1a5QuX5HGHbtSsZYZZatWJ0fuPMRER/PmxTOe+N7F88JZbl04g1GOHJgYG1O0aFH09PSYO3cuFhbJy+nWBEuXLuXEiRMAlCtXjhUrVqSrymBa8Pf3x8HBAaVSib6+PgsWLKBWrVraNitD8OzZMwYNHszFCxcoXsaEJp26UamOOWWr1iBnnrwoFQrevnrOE18fbl86z/VzJ8mWNSsuLi7Y2dlppGJlSlm3bp2Yt1+yZElWr16t9gJf6jpA+CNPnz5lxIgRYhA+e/Zsjdf8UCcaCQYgdiZ+/vx5Vq5axdkzZ/j2LeG2gZ6eHmZm5tjZ2dKjRw/2798vpmoULVoUV1dXtVXLEgSBp0+fIpfLcXd358WLFyrblStXjmLFiol7rTlz5sTNzS3DlVv98Y9qzZo1OlXxUZcRBIHLly+zctUqTp44Ic5SfqRWrdrY2AylT58+nDlzBjc3NwDy58+Pm5ubVspLy+Vysdxq9uzZWbVqlThjySjs3LmTTZs2AbFlwV1dXbW+2pJREASBa9euxaZsHj5M+P9Fpn6katVqDB06hH79+ulMGXRPT08xndHQ0JBly5ZRqdLPFRNTiqaCAYgtLR2nBps3b17c3Ny0vtqSXDQWDHxPdHQ0/v7++Pn5sXTpUsLCwihWrBiHDx+Od+I6PVM1Xr58Ka4YxKU1qcLa2prevXtTvnx5re8Dp4To6GgcHBzEIkatWrWKJ/IikTxiYmIICAjA19eXxYsXExYWRtGiRTl06FA8QSGlUsmUKVO4desWAJaWlsyePTtdZ1vv37/HxsZGzKIZM2YMbdu2TbfnqwuFQsHEiRPFg7sNGzZk+vTpGervTxdQKBQ8fPiQe/fusXDhQsLCwihSpAgHDx7UmQAgjuDgYGxsbMRDzzY2NnTp0kUjz9JkMCAIAtOnTxeLGJmamjJv3jydWHX5GeliYZYsWahduza9evWifPnylChRgiJFiiRIvUrPVI0yZcrQu3dvXF1d2bp1K0OGDFEZhbq7u2NnZ0e/fv1Yt24d9+/fzxA66nGFPOKW2M6ePcuFCxe0bFXGw9DQkBo1atCjRw/Rd4sWLZpAWVDb5zUUCgVz584VA4HGjRvTpk2bdHu+OjEwMGDChAniasDVq1c5fvy4lq3KeBgYGFC1alW6desm+m6xYsV0LhBQKpUsWLBADAQsLS0TZJJlFOLKzMcd1r1z506GkSvWuXBFVarGy5cvNfrM4sWL061bN2rU+K8++I+Khm/evGHv3r2MGjWK3r17s2rVKnx8fHT6xHOJEiUYNWqU+HrZsmW8efNGixb92uTPnx9HR0fx9fr168Vyq5pmx44d+Pr6ArF/Q9qWG04rhQoVYty4ceJrSa741+XQoUPiilr+/PkZP358hphJJ0aePHmYOHGi+Pe3efNm7t+/r2Wrfo5OfuPaSNW4ceMGBw8eBGJn1cuWLWPPnj2MGjUKMzOzeM754cMHDh8+zNixY+nZsyfLli3j9u3bYsllXaJ58+a0bNkSiFX0cnZ21kk7fxUsLCxEYZ+YmBjmzJmT6JkDdeHj4yOevNfX14+3upaRsbKyomPHjsB/RcJUnT2SyLg8evSI9evXi68dHR11buUiNcSthEPCImG6ik4GAxA/VePp06fxHEbdfPr0iQULFoivhw4dSvny5SlQoADt27fHxcWFffv2MXbsWOrWrRtP/CI4OJjjx4+LhZQWLlzIjRs3dCrPdMSIEWKebkBAAFu2bNGyRb82/fv3F7ec/v33X42Wlw4JCWHevHliKlnfvn2pXr26xp6X3gwZMoRy5coB8Pz5c/GQpkTGJyIigjlz5oiTk27dumk1C0fd9OnTR8yIe/v2LcuWLdPpLWadDQayZ8/O5MmTxYI7hw4d4vr162p/jlKpxMXFRVQorF+/Ph06dEjQLk+ePLRp04Y5c+awf/9+Jk6cSMOGDeOlbIWGhnLmzBmmTJlC165dmTdvHu7u7lqfzeTIkSOeXPGePXu4ffu2Vm36lYk7rxGXvaGp8xqCILB48WI+fPgAxM5GevToofbnaJM4ueK4bbtjx47h7u6uZask1MHKlSvFeiqVKlXSCdVOdRJ3Bi5OOv/ixYuiqqIuorPBAMSm+dnY2IivFy5cKOqsq4u9e/dy584dAAoWLJis8pg5c+akefPm/P333+zfv58pU6bQpEmTeKl74eHh/PPPP8yYMYMuXbowa9YsLl26RHh4ytXt1EGlSpUYODC2qqQgCLi4uIj1wSXUT8mSJTV+XuP48eNcvXoVgNy5czNx4sQMo4WREoyNjeNVf5TkijM+Fy5cECutGhkZ4eTk9EtWWi1WrFi8M3ArVqwgMDBQixYljk4HAwB//PEHVlZWAHz58gUXFxe1Hdq7f/9+ArnhlNafNzIyonHjxkyePFkspNSyZctECyl16dKFadOmce7cOUJDQ9XyOZJL586dxWW4oKAgFixYoNPLVhmdFi1a0KJFC0D95zV+lBv+/gTzr0jbtm1p1KgRELsCN2/ePJ0+vCuROG/evGHZsmXi61GjRlGyZEktWqRZGjduLKb46rJcsc4HAz+manh7e7Nv37409xsWFoazs7M4oPTs2ZM6deqkqc+sWbPSoEEDHB0d2bdvH87OzrRt2zZegBEdHc21a9cSFFJKj1m6vr4+jo6O5MuXD4CbN29KcsUaZuTIkWo/r/Ht2zecnZ3FAaVDhw40aNAgzf3qMnp6ejg4OIjiX/fu3WPnzp1atkoipcTExODs7CyukH4fMP/K2NnZUbp0bJnpx48fs3HjRi1blBCdDwYgYarGpk2b8Pf3T3V/giCwbNky3r59C8TKDffp00cttsaRJUsWLC0tGTNmDHv27FFZSEmhUIiFlLp378748eM5cuSI2rdCvkdV+tvjx4819rzMTo4cOXBychKX79VxXsPNzY3nz58DULZsWYYOHZpWMzMEuXLlYtKkSWJmz/bt28V0SomMwZYtWwgICABiU591oUJiehBXZj5uK+TAgQPcvHlTy1bFJ10UCL8nLepPmzdvFlOoihUrhqura7zl+ORy9uxZMXsgR44cuLm5iQVSNI1SqcTf3x93d3fkcrnKvU89PT2qVauGTCbD2tpaI1LIa9euFVdYSpUqxerVq8UzDw8ePODq1at4eXnx6tUrYmJiyJ07N7Vq1cLc3JzGjRtnSmnjtPjuvn37WLt2LQAFChTAzc1NXKFJCe7u7syYMQOI1cJYtWoVxsbGKe4nI7Njxw5xe69w4cK4ubmJAmZPnjzB3d0dLy8vnj9/TkxMDLly5aJGjRqi7/4KaZcpRZOqe8nl9u3bTJw4EUEQMDAwYNmyZVSuXDnd7dDmd3H48GFWrVoFQL58+XBzcxMniC9evEAul+Pl5cXTp0+Jjo4mR44cVK9eHXNzc5o0aaJRWW7dKxCdBH369OHOnTv4+/vz9u1bli5dmmK54sDAQFasWCG+dnBwSLdAAGKX6mvUqEGNGjWwsbFRWUhJEAT8/Pzw8/PD1dWVSpUqiYFBqVKl1GLHgAED8Pb25tGjRwQGBrJy5UrKlCnDihUruXrVHT09PUqVq0iR0mUwMDTk5fNXnDh1mrDQEPLlz8+ggQOxt7cXl74kkqZz5854eXnh5eUlnteYPXt2inz3/fv3LF68WHw9bNiwTBcIAPTo0YPbt2/j4+PDhw8fWLx4MbVr12bFypVc+OcfAEqWLU+xMmUxyGJI4MvXnDl3npDPweTOk4f+/foxevRoMWVRQvN8/vwZFxcX8YzSoEGDtBIIaJsOHTrg5eXF9evXxe+kcePGrFixkjNnTiMIAsXLmFC8bHkMs2Th39fv+OfSZT5/+kiOnDn5q3dvHBwcqFKlitpty1ArAxCbr2lraysKOIwbN47WrVsn696oqCjs7e3FZfE2bdowduzYFNugCQRB4NmzZ2Ihpbhl4B8pV66cWGHR2Ng4TSpzgYGBDBs2jKCgIO4HBBD06RM16jagda9+mMqaYfTDqosgCPz79DH/HNjFpYN7UCpiWLRwIUOGDMnQanfJJa2+GxQUhI2NjXg+xM7OLtmyqwqFgvHjx3Pv3j0AZDIZU6dOzRTfuyo+fPiAjY0NHz9+5H5AAB8/fKCKmSWte/bDomlLcuSKL3UuCAJvXjzj4qG9XNi/k2/hsWeGRo0alaHV7pKLNmfDgiAwZcoUcVnc3NwcZ2dnrX3v2l4l+fLlC0OHDuXt27c8ePCAd+/eUaFGLVr37E/dFm3IlTdfvPaCIPD+31dcPryP8/t2EBocxPTp03F0dIyneZNWMtxfwY+pGitXruTVq1fJunfjxo1iIFC6dOl46UraRk9Pj3Llyok1EDZs2ED//v2pUKFCvHZPnz4VaykMGjSITZs28fjx41RlBZQqVQqZTMaNmzfRM8zCtI27mbF1Pw3atE8QCMTZWKp8Rfo5TmPluWvUb9MeGxsbuvfooZOnY3WNAgUKpPq8xs6dO8VAoEiRIjg4OGTaQABitwfatm3LjZs3iVYombh6E3N2HqFR+z8TBAIQ67slTMrR22Eiq85dp2mXXjg4ONCuXXutpfsCmSKb59ChQ2IgkC9fPhwdHTNFAJYYefPm5c8//+TmzVt8jYhkzOI1zNt3imadeyQIBCDWd4uWKkO3EWNZedaD3/sNZerUqbRo2ZKQkBC12ZUh/0d+TNX4/mR1Yty8eZMDBw4ACUVhdJG4Qkpr1qxh69atDB06lKpVq8Zr8+rVK3bu3ImdnR19+/Zl7dq1+Pv7i2p0P+PKlStMmzaN6pZWLD1xmdoNGiXbvpy582A3ayHjl6/nyJEjdO/RQ5I5TgaWlpZiNbbo6OhkyRX7+vqKpb3j5IZ/LPKV2fD09GTM2LGUrVaTZSevYNkseauDANlz5GDQ5FlMWbeTS5cv06FDR60Ig3379o0mTZro5MlydfH48eMEcsPfH6LOjPj7+2M3bBjFy5Zn2YnLNPytQ7ID+6zZsvPXWCdmbD2A1+07tGnTVm0yxxkyGICUpWrE7dHGMWTIkAQzbl2mePHidO3aleXLl7Nz506GDRtGzZo14znQ27dv2bdvH/b29skqpPTx40e6dO1KxdrmTFyzOcFsKjrqG9sWzmawzJSetcsxsdvv3L16OUE/9Vv9xtilazl65Ei871gicQYOHEjFihWB2K2a1atXJ9o2NDQUZ2dnMcDr06dPvIJamZGQkBD+7NyZEmUrMHX9LnLni69ln1zfNZU1YcLqzVy+cpnp06enl/kidnZ2XLlyhRcvXqT7s9ODOLnh6OhoALp06YKlpaWWrdIukZGR/Nm5M3kKFeHvzXvJX7hIvOvJ9d1qFvWYsn4nd7y91bbVnWGDAVWpGjdu3EjQLk5uOG6ftl69emLxk4xI4cKF6dSpE4sXL2bPnj3Y29snKKT08eNHsZBSjx49WLp0KV5eXvFm7sNHjCAyKhr7havImi17guesmDiaY5vXImvfiQFOM9HX12eOTR/ueyX8ji2atuSPQXb8/fffUqpXMohbmcqePfZ7P336NBcvXkzQThAElixZIsoN16xZk549e6arrbrIuHHj+PjxE6MXr1G5nZUS361ZvyHdho9lwYIFKscPTbFixQo2bdpEx44d+fvvv9PtuenJ6tWrRbW9ihUrigqomZlp06bx9OlTHBa7qtwSSInvVqxlSp/xU3Bzc+P8+fNpti3DHSD8kR9TNVxdXSlYsKB4fe/evaxbtw5IW0qXrhMSEoKHhwfu7u7cvn1bjMa/J3fu3DRo0IDChQvTv39/Rs5bRpOOXRO0e+Rzh4ndfqfv+Kl0GGQHQNS3SBzaNyNvgYI47z6W4J6ob5GM7dCCemZ1OPj/7RhNEBUVRUBAAHp6elSoUCHRrZ6QkBDCw8PVmimibt89d+4c8+fPB2JTXF1dXSlevLh4/cSJEyxduhSI/b9zc3OjcOHCaX5uRubx48dUrFiRQZNn8VufQQmup8Z3FTExTOz6GyYlivKPGgZVgE6dOiVZtvbJkyfExMRgbGwsBoVbt26lbt26ann+j6T3obmLFy/i7OwMxNaZWbNmjdoyodKKtg4QvnnzhjJlytB1+Bi62I1OcD01vqtUKpnetzNGKPD8fxno1JJhVwbi6NChA/Xr1wdi01fmz58vLqk+ePBA3D7Q09NjwoQJv2QgAP8VUpo9ezb79u0TCynFFXiB/wopOTk5kb9IUWTtOqns69qZ4+gbGNCy+1/ie1mzZad555488Pbi45t/E9yTNVt2fu87mKNHjmhEe/vr1684OjpSqFAhateuTa1atShYsCB//vknBw4cEA+BxcTEcOjQIUxNTUVxE12lRYsWNG/eHIiVK547d664evP8+fN42wdjx47N9IEAgKurK7nz5ad5114qr6fGdw0MDWk/0JYL//yjNp959uwZDx48SPRf3P/zixcvxPe0eZBRnbx580YMYiFWblhXAgFtsn79egyzZKVt7wEqr6fGd/X19ekwaBhenp7cyuzBQJxccdyhlNu3b7Nv374EcsPdu3fHzMxMm6amG98XUtq3bx9Tp04VCykplUrev39Pq25/YZBIWsqz+76UMCmX4BxBhVp1/n/dT+V9jf7ojGGWrOzevVutnwegffv2LFiwgBo1ajBu3DiGDBlCiRIlOHToEF26dCFv3ryYmJiQP39+/vzzT/T19XX+XIienh4jR44UVwPu37/P1q1bE8gNt2/fnoYNG2rTVJ1AEAS2bd9O4w5dyZZd9YpQan3XqvXv5MmXXxQ1Syve3t4IgpDg3x9//AHA0qVLE1xr0qSJWp6tTWJiYpg7d64Y2DRv3jxTyA0nh23bttPgtz/ImUd1/ZvU+q5po2YULl6Sbdu2pcm+DCU6lBh58+Zl4sSJTJgwAUEQ2LRpE97e3qKIT5UqVejXr5+WrdQORkZGNGrUiEaNGhEVFcWePXu4cOEC1esl/uMS/OE9+QsnVD2Mey/4/TuV9+XIlZvyNWqlOUJVRdasWTl16hRt2rSJ9/7Vq1fZvHkzZ8+e5c2bN5QtW5ZevXoxZsyYDKE0lzNnTpycnBg9ejQKhYLdu3fz4sULnj17BoCJiUm8yp2ZmVevXvH+3Ttq1Eu8DkNqfTdL1mxUqmPOzZvq9904tm/fztGjR7G2tv5lZXi3bt0qbo8UL16ckSNHZuoU2Dg+f/7Mo0cPaTsk8f/31PqugYEBVS3qpdl3f4lgAMDU1JQePXqwa9cuFAoFnp6ewH/a8OoUZ8ioZM2aVcxrLlc18RPpUZGRGGbNmuD9LP/fcoj6FpnoveWq18LLPeFhuLSyf/9+lel0DRs2zPCz5ipVqjBgwADWr1+PIAh4eHgAsf9fkydPjrfVk5mJKzVernrNRNuk1Xcv7E3b7Cox3r59y6hRozAyMmLjxo2/ZJ79nTt3xFVBAwMDnJycUiUX/yvi7e0NQLlqmvPd3edOolAoUl3G/JfyyL59+1K+fPl4740aNSreoazMzsePHzHKmROjJGbNWbNnJ0aFbkP0/3OxVWUfxJG/cBE+BX1Ku6E/8Kvn1Xft2jVByqCtrS0mJibaMUgHiSvgpWr2FEfafLcoQZ8+qUUIqE6dOujp6Yn/ihcvTnBwMBEREVSqVCnetbh/ly5dSvNztcWXL1+YN2+e+N0NGDBAI5K5GZX/fLdIom3SOu5GRkam6dzJLzVdFgQhQV59cgV4MgvJWbLLX7gIQe/eJng/+EPsMlX+IokPxoIgaGRZsE6dOty9ezdF91y8eDHD7MOq8l1JxCk+cX6V1I91mnwXQfxhTitly5YlMjJ2Jvfs2TOioqIoVapUkjPlHDlypPm52kAQBBYuXEhQUBAAZmZmdO2aMEspM5Me425yn5MYv1QwsGnTpgSa/suXL6dq1arSadb/U6hQISLCwggLDSFnbtUVsEyqVMf3hgfhX0PjHWZ5dDd2mbZs1eqJ9h/0/h0FCxZSr9HEH1yTS0YaXHfv3p0gFW3dunXUqlUrwWpXZqVQoVi/+vzhHQWLlVDZJm2++5aChdTju4cOHQJiU5///PNP6taty+XLl8U0wl+JI0eOcP36dUCSG06MON8Nev9Opb4ApM13g9+/w8jIKE2qur/M/9itW7fEkrxZsmShQYPYQ0ZxcsWq8u4zI3EZFc/8ExcHsmrdDqVCwbk928X3oqO+ceHQHirWNqNQ8ZKJ3vvMzwcLc/VnbRw6dIiAgIAU/dNUzra68fX1ZevWrUBsqlDjxo2B5MsVZwYiIyPFv+Enfj6Jtkub795Ta8aRj48Pffr0oXjx4hw6dOiXDASePHkiluaGWEGo73VeJGK1UeIyg55qyHef+PlQu3adVJ8XgF9kZSA4OFgUbwEYPHgwbdu2Zfjw4bx69YpHjx6xceNG6VQ2ULlyZXLmysW9G+6JnsquVNsMqzbt2bFkLl+CPlKsTFkuHd7Lh39fMWz2okT7DgsN4YnfPQb37qEp8385vn79yty5c8XtrL/++ovu3bvz77//8vjxY169esWaNWsYM2aMli1Nf8LDw7lx4wZyuZxbt24RERFBdiMj7l2/St3mbVTek1rfjfoWyUNvL363H6U2+/PmzUv16tVZvnw5JUqoXsnIyPwoN9y5c2fq1aunZat0g4iICDw9PZHL5dy4cYPw8HBy5c7NvevuKoXeIPW+q4iJIcDrBr27d0uTzRk+GFAqlcyfP1+UG65bty6dOnVCT08PJycnRo0aRXR0NPv378fMzCzTa2MbGhryV+/e7D+wm652Dhj+X875R0a5LGPXspJcPnqAsC9fMK5clUlrtlLdsn6ifV8+vA+lIoYePaRgIDnEyQ2/f/8eiJUb7tWrFwYGBkyePBk7OzsiIyM5deoU5ubm4orBr0xoaCjXr1/nypUreHl5xVvR09PTo2iRIlw6tJe/xkwim5HqbaDU+K7HqWOEfvnMX3/9lWiblGJsbCwun/+KrFmzRqwYW6FChUwvNxwWFhYveP2x+FXRIkW4evIIAybNSHSrIDW+63X5PB/fvqFv375psj/DBwMHDhwQ0wgLFCjAuHHjxEMUFSpUYPDgwaxZswaA+fPn4+bmlumrZg0bNgw3NzcuH91P886qte6zZstOP8dp9HOclqw+v0VGcGLrejp07PhLzoI0walTp7hy5QoQmy0xceJEcZmvVKlSjBgxgoULFwKwZMkSKleurFZ5ZV3h8+fPeHh4IJfLuXPnjsriWvny5aNBgwaULVuWP//8k7N7ttO+/1CV/aXUd2Oiozm2yZUWLVqKBaQkkuby5cucOnUKiJUbnjx5MllVpMX96oSEhHDt2jXc3d0TBK9x5M6dGysrK6pXr07Hjh05sXU93UeOU9lfSn1XqVRyeP1qLC3rpnmLK0MHA6rkhvPnj1/BrFOnTty+fZsbN26IcsXOzs6Z+oBLrVq16NOnD1vmzaCOdRMKFk176uWupfMJfv+W2bNmqcHCX58XL17Ekxt2cHCgSJH4aUetWrXCy8uLixcvEhYWxty5c1m8eHGa9gV1hY8fP3L16lXkcjn37t1TmfVToEABrK2tkclk1KxZU/zcw4YNY/1SFyyatqS4cdk023Jw7QpePX7I/h2a0Rj41Xj79i1LliwRX48YMSJTHdAODg4Wfffu3buJBq8NGzZEJpNRu3ZtUefG0dERl/nzqdfqN0wqV0uzLSe3b+TBHU+1pKVm2GAgPDwcZ2dnMf2qW7duKiOjOLliGxsbgoKC8PLy4sCBA5k+9WXp0qWcPXeOJQ62TN2wK9El1+Rw/exJjm9Zy/z586Xc4mQQFRWFs7OzuIzYrl07ZDJZgnZ6enrY29tz//593r59i7+/P9u2baN///7pbLF6ePfuHXK5HLlcjr+/v8o2RYoUQSaTIZPJqFq1qsqgfd68eZw4eZLFDjb8vWV/olkxycHb/RL71yxl0qRJmJubp7qfzIJCoWDu3LmEhYUB0LRpU1q1aqVlqzTPx48fcXd3Ry6X4+vrqzJ4LViwIDKZDGtra2rUqKEyaJ86dSqHDx9hiYMds3YcJE/+1B+2DLh9kx2LnBk5cqRathAzbDCwcuXKeHLDSQ2Q+fLlY8KECUycOBFBENiwYQO1atWicuXK6WSt7lGgQAEOHTxI8xYtmD3kLyas2pjoPlZSyI8fYsVEe7p1746Dg4P6Df0FWbduHU+fPgVi5YZtbW0TbRsnV+zg4IBCoWDnzp2YmppSu3bt9DI3TQQGBuLu7s6VK1d49OiRyjYlS5YUB9E4QZ6kyJUrF4cPHaJxkybMHNgdJ9dt5E1FOuutC2dY7GBH61atmTYtecuymZ1t27aJgVyxYsWwt7f/ZeWG37x5IwYAiVWgLFasmLh6VaVKlZ+uOGfLlo2DBw9gLZMxrU8Xpq7fkWiabFL4XJMzf8RArKzq4+LikuL7VZEhg4Hz589z7tw5IDaXfNKkST+VGzYzM6N79+7s3r0bhUKBs7Mza9asyVC56OrGysqKmTNm4DR5MqN+a8Sw2YuwaNoyWfeGfg5mk/M0Lh89QJ8+fdiwYcMvsXytaa5du8bhw4eBWLlhJyenn8oNV61alf79+7NhwwYEQWDu3Lm4ubmRN6/qgifaRBAEnj9/Lg6icTUWfsTExARra2saNWqEiYlJin9QateuzYL58xk5ahSjfmvE0L/n0aBN+2T1E/41lK3zZ3Fu73Y6durErp07yZLIQVqJ/7h79y47d+4Efl254VevXiGXy3F3d080eC1VqpS4elWhQoUU+26lSpVYsXw5AwYMxP73JgycPIumnbolq59vEeHsXOrCia3radGiJQcPHkiTtsD3ZLhg4PXr1yxfvlx8bW9vn+wDa/369cPb25uAgABev37NihUrmDBhgqZM1XlevHjB5cuXqVe3LgEPHjDXrh+V65jTqmc/zBs3J3e++OcvFDExvHjgzz8HdnPl6H6yGBqyZcsW+vTp88vODtTJx48fxQOBECs3XLZs8va8u3Xrxu3bt7lz5w6fPn1i0aJFzJgxQye+d0EQePz4sbgFkFgJ64oVK4qzqNKlS6fpme/evePEiROxvhvwgMUOthxZv5pWPfti2aw1eQvEX35VKBQEPn7IxUN7uXRoD0pFDGvWrMHGxkYnvkNd58uXL8ydO1dUuuvfvz9Vq1bVslVpJy54vXLlCu7u7glE6+IoW7asuHqVmuD1e4KDg9m/fz9161ry8OFDVjk5cHyzG6169KV+q9/JVyh+qXKlUsnrZ0+4dHgfFw7s4lt4GAsXLsTe3l6tE7AMFQxER0fj7OwsirC0bNmSZs2aJft+Q0NDnJycsLW1JTw8nPPnz2NmZkbLlsmbDf9KxO1bR0ZGxp4GdnKiXLlyrFixkhUTYnOti5UuQ9HSxugbGBIe8oXnD+7zLTKCIkWLMmb0aIYNGybVfUgmCoUCFxcXQkJCgNgCS+3atUv2/fr6+jg6OmJra8uXL1+4du0aR48epUOHDpoyOUmUSiUBAQHiLOrt24QyqhC7qhE3iKrLV+JW9sLCwsiaNSv29qMwMzNjxYqVuE4dz5op4yhSohTFjE0wMMxCxNdQXjy4T0R4GPkLFMB26BBGjhyZ5oAksyAIAosWLeLTp9iaI6ampnTrlracdm0SF9CEhYUxYMAA/v33X5XtKlasSKNGjbC2tlbbAcnvU+GzZMnCwIEDad68OStWrmTjnKmsm+lEoWLFKW5SHsMsWYgM+8rLRwGEhYaSJ29eBvTvz8iRIzWiSpqhgoHNmzfz4MEDIHafccSIESnuo3jx4tjb2zN37lwAVqxYQbVq1ShZMnF1p1+RH/et7ezsyJYtG3/88QfPnz/Hw8MDLy8vAgMDiYmJIXe5Mgzp0wtzc3MaNGiQKdOI0sKePXvEymWFCxdmzJgxKZ5dFCpUiPHjxzNlyhQA3NzcqFmzJuXKlVO3uSpRKBT4+vri7u6Ou7u7WHzle/T19alRowYymYyGDRtSuHBhFT2lDVX71jlz5qRNmza8evVK9N0XL14QHR1NLpNSDOjRVfRddS2rZhaOHj3KtWvXgFghpYwoN6xUKrl//z5yuZzg4GAgVhjox0CgWrVqYvCqiTReVanw+fLlo2nTprx584arV6/i5eUl1rPIUaYEfbp0wtzcnIYNG2p0WybDBAOenp7s3bsX+G+Gn9r9/mbNmuHl5cXZs2eJiIjA2dmZpUuXZpp9w5/tW5uYmGBiYkKvXr20ZOGvhb+/P1u2bAFifywnTJhAnjypOwFfr149OnXqxKFDh0S54lWrVmlM6jYmJoa7d+8il8u5evWqKO71Pfr6+tSpU0cMAH5M71UnP9u3Ll26NN27d6d79+4asyEz8fTpU9zc3MTX48ePF3X2dR2FQsG9e/dE341b2fgefX19atasKfquJj+bqlT4fPnyideLFy9Oly5d6NKli8ZsSIoMEQz8KDc8aNAgKlWqlKY+R4wYgZ+fH//++y8PHz5k8+bNDBkyJK2m6jxp2beWSDlfv37F2dlZTEXq1atXmjMBBg8ejI+PD0+ePOHly5e4uroyevRoNVgbS1RUFLdv30Yul3Pt2jVCQ0MTtMmSJQvm5uZYW1tjZWWV6uAmJYSEhMQrk/ur7FvrKpGRkfHkhjt16qTzcsMxMTHcuXMHd3d3PDw8VAavceTKlYuNGzdqNHiN48dU+O7du6u1DoY60PlgQKlUsmDBAnFpx9LSkj///DPN/RoZGTF58mRGjRpFTEwMe/fuxdTUFAsLizT3raukdd9aImUIgsCyZct49y62BGn16tXVIncbt5ozfPhwIiMjOXHiBGZmZjRq1CjVfUZGRnLr1q14Wuo/ki1bNiwtLZHJZNSrVy9dT5LH7VvHbU1k9H3rjICrqysvX74EoHz58gwePFjLFqkmKioKT09P3N3duXbtGl+/fk3QJi54lclkbNiwgaCgILJnz54ugQAkTIXv169fujw3Jeh8MHDo0CFu3boFQP78+Rk/frza9qsqVqzI4MGDcXV1Bf6TK04vB0lv9u7dm+Z9a4nkc+bMGVEZLFeuXEyaNEltp3/LlCnD8OHDWbQotoDJkiVLqFKlSgIVw6SI01J3d3fn1q1bKktEGxkZUa9ePRo1aoSFhYXW9tuPHTuGh4cHkHH3rTMSV65c4cSJE0Cs3LCTk5NOnROKiIiIF7yqquyZPXv2eMFr3Lbypk2b0tXWH1PhnZycfpoKrw10z6LvePToEevXrxdfOzo6qv2HulOnTnh5eXHr1i2Cg4NZsGABs2fP/uUGGn9/fzZv3gykfd9a4ue8fPmSVatWia8dHBwoWrSoWp/RunVrvLy8uHTpklj9cOHChUkGHKGhoVy7dg25XJ6olnquXLmwsrJCJpNhbm6u9R+BZ8+eiQE7ZKx964zIu3fv4skNDx8+nDJlymjRoljCwsK4fv06crkcT0/PBIWAIPbHtn79+lhbW2Npaan1stGqUuF1NQNLZ4OBuPKY38sNa2IJX19fn/Hjx2NjY0NwcDC3bt3i0KFDdO7cWe3P0hZxuvbq3LeWSJyoqCjmzJkjzrR///33NC3hJ0acXHFAQABv377F19eXHTt2JKheFhwcLBYC8vb2TrIQkEwmo06dOjozc8mI+9YZmTi54bil9iZNmtC6dWut2RMSEoKHhwfu7u7cvn070UJAcb5ramqq9eA1jh9T4Vu1apWiVPj0Rjf+4lWwcuVKMe2jUqVKGtVjz58/vyhXDLB+/Xpq1ar1S1QwEwSBpUuXinng6tq3lkic9evXi2mbZcqUSVJuOK3EbT84ODigVCrZsWMHderUoUSJEmIKYGKFgAoWLCiKACWmpa5tXF1defHiBQDlypXT2X3rX4Xt27fj5+cHaE9u+PtCQN7e3ip9N7FCQLqEOlLh0xPd+waBCxcucPbsWSB2z9LJyUnjaX/m5uZ069aNvXv3EhMTw5w5c1izZk2Gz0n+ft86Z86cat23lkjI9evXOXToEBB7aGny5MkaX6qsVq0a/fr1Y9OmTSiVSiZMmCCuqP1I0aJFRRng5GipaxO5XB5v3zqzlslNL75P29TX12fSpEnkypUrXZ794cOHeIWA4jJGvqdQoUJi8Fq9enWdHsdUpcLr+m+JzgUDb968YdmyZeLrUaNGpZsgUP/+/bl79y4PHjzg33//ZeXKlYwfPz5dnq0JXr16pfF9a4n/+DFt08bGRuOCQIGBgaIKYBw/BgKlSpUSB9GKFStmiEOj79+/Z/HixeLrYcOG6cS+9a9KSEgILi4u4iy8X79+VKuW9hK7SZHcQkBxIkC6HrzGoYlU+PQgXYKBiIgI7t69i7+/Pw8fPiQ8PJzo6Gg+ffpEwYL/aYjHxMTg7OwspjW1aNGCFi1apIeJQOxMzsnJCTs7O8LDwzl79izm5uY6vc+TGD/uW//2229qKXOZ2fj27Rs+Pj74+fmJvhsVFcX79+/jndyPS9v88uULEFsE6o8//lC7PXFa6nF1ABLTUgeoW7cugwcPTrOWenrz475148aNadOmjZatynhERUXh6+vLvXv3RN/99u0bb968iXeITRAEFi9ezIcPHwCoU6eOxkSbXr58KQavjx8/VtmmdOnS4upV+fLlM5TvaioVPj3QWDAQExPDiRMnWLVqNRcu/CMeWjLMkgWFQkFAQACFChWievUa2Nra0KdPH/bv309AQAAAJUqUYOTIkZoyL1FKlCjBqFGjmDdvHgDLli2jatWqOnsCNDE2bNjAkydPgNh9azs7Oy1blHFQKpWcOXOGVatWc+bMaXGmbWiYBYUy1neLFi1KxYqVsLEZyoABAzh79qyYtlmoUCHGjRuntkFMEAQePXokDqJJFQIyNjbm/PnzAKI9GWkwBdixYwe+vr5A7LbG6NGjM9xn0BaCIHDhwgVWrV7NiePHiYqKAmJ9V/l/3y1RogQmJmUZOnQIgwYN4saNG1y9ehWAPHnyMGHCBLUtwQuCwLNnz0TfTSx4LVeunLh6ZWxsnGH/vzWZCq9p9ARVmzNp5NatW/QfMAB/Pz8q1Taj0R+dqVjLDOPKVciSNRtKpZK3L57xxM+HG+dOcfP8KYyMcmBsXIZixYphaGjIsmXLqFy5srpNSzbz588Xc0OrVKnCkiVLdPKQiipu3Lgh6tdnyZKFFStWaKSwxa/IvXv36Ne/P3du36Zc1Ro07tSNSrXNMK5clWzZjRAEgXevXvDEzwfPC2e5duY4hgaGGBuXoWTJkujr67NgwYI0Z2vEFQK6cuUKV69eTbQQULVq1bC2to5XCGjVqlWi3LSJiQkrV678aZlkXcHHx4fx48ejVCrR19dn8eLFVK9eXdtmZQgePnxI//4DuHbNA+OKlWnSqTuV6phTtmp1shnlQBAEPvwbyBM/H7wunePqyaPoIWBiYkKpUqXQ09Nj5syZWFlZpckOQRB4+PChuHoVJ7bzI5UqVRK3ANRVCCg59OzZk48fP1KoUCF27dqltn4fPXokitgBzJ07N0OJ2Kk1GIirtT5t2jTKVq3O4GlzqVjL9Kf3Bb17y/ZFzlw+up/ChQuzaNEi+vTpoy6zUkV4eDh2dnaiI/fo0YNBgwZp1abk8OnTJ2xsbMTl6uHDh9OxY0ftGpVBWL58OePGjaO4STmGTJ9HVfO6P52hfPn0kd3LF3B2zzYKFizIzJkzGTZsWKqeH1cIKG4WlZiWelwhIGtra5X59lFRUYwcOVLMaGjfvj2jRo1KlU3pSUhICLa2tuJydf/+/endu7eWrcoYbNy4keHDh1OgaHEGT3OmVoNGP/Xd0M/B7F+zjBNb15EvXz4cHR3FjKqUolQq8ff3FzNY4lQ3f6R69eqi72rr/JImgoGIiAjs7OzEDLhu3bplOHl7tQUDgiAwceJE5s+fT5dho+lq54BhCjMAbl04w9JxI6hTuxbnz51LV7lTVTx8+BB7e3tiYmLQ09Nj3rx5Oqcn/T1KpZKJEydy584dAOrXr8/MmTMz7JJbeuLs7MzkyZNp128of42dRJasKZtJ3/W4wqLRNpQva8LlS5fiFSBJipiYGLy9vXF3d0+0EJCBgYFYCKhBgwbJEt568eIFw4cPF4VZpk+fjrW1dUo+UroiCAIzZswQl6tr166Ni4uLTp8Y1xVWrlzJyJEjadG1NwOdZpDNKGUF3AJu32T+yMEUKVgAd7k82SqWcYWA4lavgoKCErTR19enVq1aWFtba7wQUHLRRDCwYMECMQOuUqVKGbLwndqCgXXr1jF06FAGOM2kXd/4ucAvHz1g78pFPPHz4fPH92TLbkSpCpXoMNAOy2at4rV95HOHGQO60bZNG/bv26f1H7J9+/axdu1aILbkpJubW7IH+vRm9+7dbNiwAYjNIXdzcyNv3rxatkr32bNnDz169KD7yHF0Gz4m3rWU+O6LB/eZ3q8L9SwsOHv2TKK+GxUVhZeXF3K5nOvXrydZCEgmk1G/fv1UqUWePHlSVJLLnTs3rq6uKZIrTk+OHTsmKrXlzp2btWvX6sQPh65z6tQpfvvtN9r3t6HfhGnxfC4lvvvmxTOm/dWJiuXK4e4uT3RLNDo6Gm9vb+RyOR4eHuIK5PcYGBhgZmaGtbU1DRo00LnxUt3BwIULF5g7dy4Qmwq/Zs2adMuAUydqCQZevHhB9Ro1sGr7B3azFia47nX5H05u20DlOubkL1KMb5ERXD97gvueN7CZMZ9W3eOL4HicPsai0Tbs2rWLHj16pNW8NKFUKpk8ebJYg7pu3brMnj1b60HKj9y/fx8HBwcUCgV6enrMnz+fOnXqaNssnefdu3dUq16dKpYNGLPENcH/a0p99478ErOH9MLV1RUbGxvx/YiICDw9PX9aCKhu3bpYW1urpRCQIAjMnj2bK1euAFCzZk0WLFigc7PtZ8+eMWLECPGw24wZM2jQoIGWrdJ9Pn/+TPUaNShatiKT1+1Is+8G3L7FlN4dmTdvHo6OjuL7yS0EZGFhIQavuXPn1syHVgPqDAbevHmDra2t+Pc8YcKEdM2AUydqCQa6dO3KlavXWHzsAjlyJc8JFAoFjp1bE/XtGytOyRNcXzTahode13n54oXWxRqCg4MZOnSouIRrZ2enU+kiYWFh2NraiofMevXqxYABA7RsVcZg0KBBHDh8hCXHL5G3QMGf38DPfXfN1HFcP32MBwEBBAQEIJfLuXXrVqJa6vXq1UMmk2lES/3r16/Y2tqKe7h9+/bV+nmc7/n27RsjRowQT5l36NBB55XadIWxY8fiunYtS45dpFDx5M1Ef+a7W1xmcGbnZu7fv8/Lly9xd3dPshBQ3bp1kclk1K1bVywEpOuoKxiIiYnBwcFBzIBr0aIFEyZMUJeZ6U6aj8cHBgZy6OBBBk2dk+xAAGKXkgoWK8ET37sqr/ccPYGRbazZt29fAq319CZ//vw4Ojri5OQE/CdXXKFCBa3aBf+VyY0LBKpVq6ZTg70u8+nTJ3bu3EnnYQ7JDgTg577bfcQ4Lh7cQ4sWLVQuF+bOnVssBGRmZqZRVb04ueIxY8agVCrZvn07pqam1KhRQ2PPTAlubm5iIFC2bFmGDh2qXYMyCGFhYazfsIHWPfsnOxCAn/tuF7vRnN65mTZt2qgUecqRIwdWVlZYW1tjYWGh9UJA2mTLli1aT4VXJ2kOBjZt2kQ2IyMat/95YZ/I8HCivkUQHhrKrQtnuSO/SMO2qoVZSpiUo451Y9zc1mo9GIBY8YiuXbuyb98+oqOjmTNnDqtXr9b6qsW5c+e4ePEiEPuHOmnSpAyTAqltduzYgUKppHnnnj9tmxLfLVC0GJYt2uB3TS4GA3Fa6tbW1uleCKh69er07duXzZs3o1QqcXZ2xs3NTetLue7u7hw7dgyI3SKR5IaTz/79+wkNCaFV958H/inx3Zx58iJr/yceJ49QunRp9PT0dLYQkDa5ffs2e/bsAWIDLCcnpwyzMpIYaR6RrlyRU71uA4ySoWG9xWUGZ/dsA2JPmdZr+RuDp85JtL15k5Zsmz+TqKgonXDAAQMG4O3tzaNHjwgMDGT16tWMHTtWa/YEBgayYsUK8bWDgwPFihXTmj0ZDXd3dyrVNiNvwZ8fVEup71o2a831Mydo3bo1LVu21HohoB49enD79m18fHz48OEDS5YsYerUqVo7+6JKbtjY2FgrtmRE3N3dMalSjSKlSv+0bcp9txX/7N+FtbU1f/zxB7Vq1ZImGN/x+fNnXFxcxPoJgwYN0qomjrpIkzSSIAh43faifPVayWr/e7/BTNu4m5HzlmEqa4ZSqSBGRUnKOMpXryVKauoCcXLFcasBp0+fFmfl6c2PcsNt2rShSZMmWrElo3LL04uy1TTnuxBbAKt27dpaP7RnYGDAxIkTxdUAuVzOyZMntWKLQqFg3rx5YhaFTCajbdu2WrElo+Lp6UXZajWT1Talvlvu/75bp04dzMzMpEDgOwRBYMGCBWIapbm5+S9T7j5NwUBERATBQUEUMy6brPalylWkdoNGNOnYFSe3rUSGhTHXrp/KClWA2O/Lly/TYqZaKVWqVLy9oaVLl/LmzZt0t2Pjxo2itnfp0qVTLXSTmQl89ZLixibJapti3y0T268u+W7hwoUZN26c+Hr16tVJ1jbQFDt37uTevXsAFClSBAcHB53LztF1Xr56SfEymhl3CxQpRtZs2XXKd3WFQ4cOcfPmTQBRqCmjyA3/jDR9ijjZRYNURo71W7fj8T1vXj97ovJ6XEQanUQUqw1atmxJ8+bNgVilwrlz5yZaMlYT3Lx5kwMHDgAJVyskkocgCMTExGBgmDphkJ/5roGO+m6DBg3EAkpRUVE4OzurzHLQFL6+vmzfvh34r0yuts8uZERiYmLQN0zdatPPfFdPTw/DLIY657va5vHjx6xfv1587ejoSIECBbRokXpJUzBgZGSEnp4eYSEhqbo/6lvsEnf414SiK4DYry4OFiNHjqREiRJAbI7/1q1b0+W5QUFBLFiwQHw9ZMgQnchqyGjo6emRM1cuwkITiqYkh5/5bnio7vru0KFDKVs2dlb57NkzUVRL04SGhuLs7CyWye3Tp4/OZDVkNHLlzEW4CrGq5PAz342OiuJbRIRO+q62iIiIYM6cOWKA1KVLFywtLbVslXpJUzCQJUsWKleuwvMAvyTbffn0McF7MdHRXD68j6zZs1OqvOpaz88CYs8K6OKPXc6cOXFychL3gnfv3i3KAGsKpVKJi4uLqHdQr149qe5AGqhZoybP72vId//fry4WiIo7uR9XvOjo0aN4eHho9JmCILBkyRKx7kDNmjXp2fPnWRwSqqlZU3O+++pRAAqFgnLlyqnF1l+B1atXi9VCK1asyMCBA7VskfpJ88kQS0sLrnp6JdnGdbojEV+/Us2iHgWKFuPzxw9cOXaQf58+pt+E6RglorT28O5tsmc3YtSoUaIym5WVldZrFsRRuXJlBg4cyLp16xAEgXnz5rF27VqNSQDv37+f27dvA7HSyOosk5sZsbAw58DRYwiCkOj3mFrffXT3NoaGhkydOhVzc3NRmjU1ssKawNjYGDs7O5YuXQrAwoULcXNzo3Dhwhp53smTJ5HLY0VucufOzaRJk7R+qDIjY2FhzipXNxQKRaLfY1rGXT09PVxcXDh//nyKamL8ily8eJHTp08DsUJLTk5OGa7uQHJIswLhwYMH6dy5MwsPnaVsVdVLfu4nDvPPgV28fBhA6OdgjHLmolz1mvz210Asm7VWeU9MdDQ2TS3ImS0rVatWFd83NDTE1NRUdFBta+8rlUomTZok/khrqjjQgwcPsLe3F+WGdb1oUkbgn3/+oUWLFszcdpDqlvVVtkmN7yqVSka0bghRkdSs+d+Jb319ferUqSOWHNb24CoIArNmzRJ/pGvVqsX8+fPV/iP9/Plzhg8fLsoN//333zRs2FCtz8hseHp6YmlpycTVmxPUGYgjNb4LMP7PVoS8f0edOv+V4U5OtcyMQkoUCH+UG3Z0dKRly5bpYWa6k+ZgICYmhjLGxlSpZ82IuUvVZBbIjx9i6bjhODo68uzZM4KDgxO00dfXp3bt2shkMho2bKi1wxxBQUHY2NiIy/fqLhscFhbGsGHDMlw5ZV1HEASqVKlKfuNyOK7YoLZ+vS7/g7NNH0aPHs3bt2/5+DHhcq2enl68wVVTM/KfERoaio2NjcbKBn/79o2RI0fy7NkzIOOUU84IWFrW5ZthNqZv2qO2yUfA7ZtM7tWRYcOG8eXLl0RLEVerVg1ra2tkMlmG0zZJbjAQExPDmDFjuH//PgDNmzdnwoQJv+xqrFpqE8SV0Jy59QDV61ql2ajQz8GMad8Uq7p1OX78GAqFAn9/f7HOe9zA9T16enrxamWnd3W2mzdvMnnyZCD2LMWKFSvUtl88b948/vnnHwCqVKnCkiVLpNxfNbFt2zb69u2b5AwrJUSEhTGuY3MqmBhz5fJlBEEgICAAd3d35HK5KBv9I1WqVEEmkyGTyShevHia7UgJvr6+jB07FqVSib6+PosWLVLbwb4VK1Zw9OhRAExMTFi5cqV4VkEibRw9epQOHTpgv2AljdqnvVZKdNQ3HDu3oUDOHHh63kJfX59Hjx6J427cnvmPVKxYUfTdUqVKpdkOTZPcYGDjxo3i9eLFi7NmzRqd2aLWBGoJBpRKJY2bNOHx8xc47zmRIp13VX0tdrDF77ocfz+/BNrugiDw4MED5HI5crk80Rz/KlWqiJFr3Kl/TePq6iqm/JUuXZpVq1alOeXv3LlzzJ8/H4iVG3Z1dU33H4tfGUEQaNeuPdc9PZm37yQFi6b+uxUEgdVTxnLt5BF8fHwSHHwVBIEnT56Ivvvq1SuV/VSoUEH0XVX68Jpg27ZtYkZMkSJFcHNzI1cyVEWTwsPDg+nTpwOQNWtWVq1ahYmJSVpNlfiOnr16ceLkKebtOylqW6SWTXP/5vSOjXh5eVGrVnwxLkEQeP78uei7ielTmJiYiIGBiYmJTs6ikxMM3LlzhwkTJiAIAgYGBixdupQqVaqks6Xpi1qCAYhNUapvZUWuAoWZsmFXqgIChULB2r8n8M/+Xezbt++nyk5xg2vcrCsxkYxy5cqJDqpJydOoqChGjx7No0ePAGjbti1jxoxJdX+BgYEMGzZMrBg2adIkmjVrphZbJf7j9evX1LeyQjDMyrRNe1IVEAiCwBaXmRzb7MamTZvo37//T9u/ePFCnHU9ffpUZTtjY2Osra1p1KgRZcuW1djgqlAoGD9+vCgG1KhRI6ZMmZLq53348AEbGxtRZdDe3p527dqpzV6JWD59+oSVVQNCIiKYtmkvxUqnfHwTBIF9qxazZ+Uili1blqxtnMDAQDEwiBvvfqRkyZLiuFuxYkWdCQx+Fgx8+fKFoUOHiiqDgwcPpnv37ultZrqjtmAA4N69e7Ro2RJB3xDbWQuoY90k2fe+ffWC1ZPHcN/zBps2bUpVcaIXL17g7u7OlStXEh1cy5QpI24llC9fXu0OGhgYiJ2dnSgTPGXKFBo3bgzErnr4+vri6emJj48PoaGhGBoaUqpUKSwsLKhbty4FC8YGUdHR0djb24t/aK1bt46nHiehXh4/fkyz5s35Gh7B0Bku1G3eJtn3fnr7mjVTx3NHfpGVK1cyfPjwFD8/MDBQDGofPnyosk2JEiXEwbVSpUpq9933799ja2sr/oA7ODjw22+/AbE/GP7+/nh6enL37l2+fPmCgYEBJUqUEH03bmtOoVDg6OiIj48PANbW1kybNk1nfgx+NV69ekXz5i14++EDg6bMxvr3jsn+rj9//MC6GZO4fu4kzs7OTJo0KcXPf/PmDe7u7ri7u+Pv76+yTbFixWjYsCEymYyqVaumq2pf3Gqyp6cn3t7eHDp0iG/fvpEvXz7mzJlD3bp1xdVWQRCYNm0a169fB8DMzIy5c+f+MiqDSaHWYABi5VcHDhzEP/+cx6p1O37rM4iq5nUTdc63r15wdvdWzuzcQtEiRdi0aSNNmzZNsx2vX78WZ11xZSZ/pHjx4mJgUKVKFbUNVmfPnhWFgXLmzImLiwvHjx9n9Zo1PH3yBD09PUqYlCNXnrwoFDG8ffmCryFfMDQ0pGOnTowcMYKAgAD27dsHxEog60KFxF+dt2/fMmTIUI4fP4ZF05b81mcQtaxkifrFh9eBnNu7g9M7NpInd27Wr1sn/nimhXfv3omBgb+/v0rZ2CJFiohbCdWqVVPbYOXu7s6MGTOAWD0CFxcXLly4wOo1awj4/0Gq4mVMyJO/AEqlgneBrwgJDkJfX5927dszYvhw3r17x5YtW4BYCWRXV1edSan8Vfn06RPDR4xgz+7d1G7YiN/7DsFU1jRRvwh+/45z+3ZwavtGshoa4LpmjVo09j9+/CgGBvfu3RMFpr6nYMGCou9qsoBXREQE27ZtY9Wq1fj4xJZsLla6DDnz5EOpVPLx7b+EBgejp6dH69ZtGD58GNHR0axevRqIlRt2dXUVJ2i/OmoPBiA2utq4cSPz5rnw+PEjipYqTfmadTCuXI0cOXMRHRXF6+dPeOZ3j6f3fcmbLx9Dhwxh6tSpad6nVMX79+/FwdXPz0/l4Fq4cOF4g2taHDROc+DChQt8+PCBx0+eEBUVhVXrdjTr3IMKNU3j5fgKgsC7wJd4XTzH2T3bCHzyiGLFilGpUiVy5szJ8uXLdVJ46VdEEAR27drFHGdn/P38KFy8JOVr1sGkSjVy5s5DTHQ0b14845m/D0/87pEjZ04GDhjA33//rZFUwU+fPnH16lXkcjk+Pj4qB9cCBQqIs65atWqleXBdvnw5x44d49OnTzx+8oTwsDDqtmhL8y69qGxqTo5c/ynTCYLAh9f/ckd+gbO7tvD8wX2KFC1K5UqVMDIyYuHChfHSKyU0y6FDh5g5cxbe3ncoUKQoFWqZUrZKdXLmyYtCoeDdq+c887vHYz8fsmbNSt8+fZg1a5ZGslmCg4Px8PBALpfj7e2NQqFI0CZfvnw0aNAAa2trTE1N1XYw2t3dnQEDBvL06RPMm7SgRdfeVDGzJFfefGIbQRAIevcG76uXObtrC499fShcuDCVK1cme/bszJ49m3r16qnFnoyARoKBOJRKJRcuXODEiRN4enrh6+dLRHg4WbJmpWzZclhamNO4cWO6dOmSbrWgg4KCxMH17t27KgfX/Pnzi4NraivOhYaGYmlpyYMHDzBr1AzbmfMpWOznBxkFQeDy0QNsmDUZZUwMs2bNlLYHtIAgCMjlco4ePYqnlxf37t0j7OtXDLNkwdjYBEsLc2QyGd27d9dIAKuKz58/4+Hhgbu7O7dv31Y5uObNmxcrKysaNWpEnTp1UiWOEhkZSf369bl79y7VLa0Y5rw4WXvRgiBw/exJ3KY78i0inAmOjsycOTPFz5dIG4IgcPPmTQ4ePIinlxc+Pj58DQ3FwNCQkiVLUdfSgoYNG9KzZ89002kJCQnh+vXryOVyvLy8VNY9yJUrF1ZWVshkMszNzVNdtt7FxYVJkyZRuY45dnMWUapcxWTd53X5H9ZMGUvo52CG2dmxbNmyVD0/o6LRYEDX+fLlixi53rlzR2WxoTx58sSLXJPjoIIgYGNjw/r16xk8dQ6te/ZL8RZE8Pt3ONv15dO/r7h86RK1a9f++U0SmYbQ0FBxcPX09FQ5uObMmTPe4JqclD5BEHB0dGThwoX8NdaJDoOGpXgLIiT4E/NHDOL5fV/+OX8eK6u0pxtL/DqEhYVx48YN3N3duXnzpspCWUZGRtSrVw+ZTIalpWWyt0jnzJnDlClT6GxrT/eR41I8kQsLDWHJGFv8bnhw4sQJWrRokaL7MzKZOhj4nq9fv3L9+nXc3d25deuWqJb2PTly5MDKygpra2ssLS0THVxdXV2xs7Nj+JzFNOvcI8nn7nddxq6lLpSuWJmlxy7GuxYWGsKM/l2J/hqC7717UuEQCZWEh4dz8+ZN5HI5N2/eFA+vfk/27NnFwbVu3bqJDq67du2iV69eDHCaSbu+g5N8blK++y0inNlDevPh5TP8/fwytGKdhOaIjIzk1q1byOVybty4ISr9fU+2bNmwtLREJpNRr169RHP9T5w4Qbt27eg+chzdhiedxZWU70ZHReEyfABPfG6rTG//VZGCARVERESIg+uNGzcSHVzr1q0rDq5x2xzPnz+nRs2aNPitI7Yz5yf5nE9vXzOybewBtcIlSydwSoB3gS8Z+0dz+vb5C1dXV/V8QIlflsjISDw9PXF3d+fatWsqB9esWbNiaWmZoNbH27dvqVa9OtXqWzNmcdK+lhzfDX7/Dof2Tfn9t7bs2rlTPR9Q4pclKiqK27dvI5fLuXbtmpjV8j1ZsmTBzMwsQa2P4OBgqteoQbHylZm8dnuSK7HJ8d2vXz7j0L4p9czNOXHieKbIhJGCgZ/w7ds3vLy8RAcNCwtL0CZLlixYWFggk8nYsGED/1y+wpLjl+IdtFLF4jG2hAQFoVQoCPkcpNIpAU5u38iG2VPw9/ePV6dBQiIpoqKiuHPnDu7u7ly9elXl4GpoaIiZmRkymYyDBw+yZ/8Blp64/FOdkOT67qUj+1kxYRTXr1/PVIexJNJGTEwMd+/eRS6Xc/XqVVHq/Xvian3IZDIuXrzIGjc3lh6/RKHiSc/kk+u7ty6cYd6wAZw9e/aXrUfwPVIwkAKio6O5c+cOcrkcDw8PQkJC4l2PiorC/epV/hrjRIdBdkn25XfrOn/378rCg2fZMHtKkk4ZHfUN26aW9O3dK9MdapFQDzExMfj4+IiD64+1PmJiYrh69SodBg+np71jkn2lxHcVCgUjWzegTfNmbN68WV0fRyIToVAo8PX1FVMWf6z1oVQquerhQfMuvRg0ZXaSfaXEdwVBYFzHFtSuWpnDhw6p7fPoKr++koIayZIlC3Xr1mXs2LHs3buX+fPn0759e7FA0tu3b9HT06PZn0mrVSkUCjbMnkKLLr0wrvzzmX6WrNlo8md3tmzdqjL7QULiZ8StANjb27Nr1y4WL15Mp06dxJSy9+/fExMTQ8tuSRcpSqnvGhgY0KLrX+zevVtU0pSQSAkGBgbUrl2b4cOHs2PHDpYtW0aXLl3EAkkfP37kW2QkrXokLVSXUt/V09OjZfc+HDt6lE+fPqnls+gyUjCQSgwMDDA1NWXUqFHs2rWLJUuWkDdvXspWrUHu/ElXTzy7eysfXgfS4yczsO+p3aARXz5/TlSdTkIiuRgYGFCzZk2GDRvG9u3bWb58OUWKFKG4cdmfLrGmxndrNWjEt2/fREVCCYnUoq+vT7Vq1bCxsWHr1q2sXr2aUqVKka9QYUpXqJTkvan1XaVSiZeXV1pN13mkYEANxNX6Dgn9SoWadZJsGxocxO7lC+lqNzpF9RvKVYsVbvH09EyLqRIS8dDX16dq1apERERSoZZpkm1T67vGlatgmCWL5LsSakVPT4+KFSsSE6PQ2LhbrIwJOXPnzhS+KwUDauT9+3cUKp60sNDOZfPJlS8fbf8amKK+c+XNh1HOnCrLN0tIpJW3795R6CeiWKn13SxZs5GvYCHJdyU0wtt3mht39fX1KVisRKbwXfVoP0oAqJQ5/p7Xz59yfu92BkyaQfD7d+L7UVHfUERH8z7wFUa5cpE7n2pZWz09PenMgIRGkHxXIqOicd+FTOG7UjCgRvLly8+XJA6aBL17i1KpZMOcqWyYMzXBdbsW9fi972AGOiWUcI0MDyciLEwj+vcSEgXy5+dL0MdEr6fFdxUxMYQEB0u+K6ERChTQ3LgrCAJfgj5lCt+VggE1Ym5mygP/e4leL1OpMo4rNyR4f9ey+USEfWWg00yKlTZRee/zAF8EQcDUNOl9XQmJ1GBmZsrl67cSvZ4W3/336WO+RUZIviuhEcxMTdl94GCi19Piu5/evubzp4+ZwnelYECNWFhYcPL0bL5FhJPNKGHhpTz5C1KvRdsE75/Ysh5A5bU4/D1vkC1bNqpXr64+gyUk/o+FhQVbtm4l9HOwyuXSNPmu1w309PQyxYAqkf5YWFiwZMkSPr19rbIYXFp8977nDfEZvzrSAUI10q1bNyLDw3E/eUSt/SqVSv7Zv5OuXbumupKXhERS/Pnnn+jr6XHp8D619isIAv/s3cHv7dqlW4U8icxFu3btyJEzJ+f3qV/y+vy+HcgaNcoU9QkkBUI189tvv+P/5CnzD5zBMBXlY1Vx7cwJFtoPwcPDQ6oAJ6ExevXqxUX3qyw+dpFs2ZNXJe5n3PW4wsyBPTh16hRt2rRRS58SEj9iZ2fHnv0HWHZKTs7cedTS5yOfO0zs9ju7d++me/ekheR+BaRgQM14eXlRr149ug4fQ9dhDmnuL/RzMGPaN6W+pSXHjx/LFAUzJLRDQEAAderUoXWv/vSbMD3N/UWEhTGuY3MqljXh0sWLKS6FLCGRXF68eEGNmjWp36Y9drMWprm/6KhvOHZuQ8HcOblx/TpZ1DSx02Wkv041Y25uzsSJE9m/Zin3rl9NU1+KmBhWTRqNIjqKdevWSoGAhEapUqUKs2bN4tjmtXhePJemvpRKJW7THfny6SObNm6UAgEJjWJsbMyihQs5v28n8uNpqyMgCAIbnafz5vlTtmzenCkCAZCCAY0wbdo0mjRugsuw/tz1uJKqPqK+RbJk7DDuyC+yc8cOSpRIWlRDQkIdjBkzhg4dO7Jo9FBu/nM6VX3EREezevIY3E8cZvOmTZQvX17NVkpIJGTIkCH07duXFRPtuXIs8eyCpFAoFGx0nsbZ3VtZs2YNNWvWVLOVuou0TaAhwsPD6dTpT86fP0e7/kPpMWp8svdhH/ncYdWk0bwPfMmePXvo0KGDhq2VkPiPb9++0at3bw4eOECbXv34a+wUjHLmTNa9zwP8WDXJgZePAti8eTO9eydd+EhCQp3ExMQwePBgtmzZQtNO3RgwaQY58yTv4Grg00esdhrDw7u3Wb16Nba2thq2VreQggENEhMTw6JFi5g2bRp5ChSiZY8+NP+zB/mLFE3QVhETg+9ND87s2sKtf85gambG5k2bqFGjhhYsl8jsKJVKVq1axYSJEzHKmYvmXXvTvEtPCpcolaCtQqEg4PYtzu7awrWzJ6hSuQpbtmzG3NxcC5ZLZHYEQWDjxo04jBmDvmEWmnXuSYtuvSlW2jhBW6VSyWOfO5zZtZWrp45gXMaYTZs2Ym1trQXLtYsUDKQDAQEBLFiwgF27dhEREUHRkqUxrlqdXHnyolAoePfqBc/v+xEZEU616tUZOWIEgwcPxtBQkoGQ0C5Pnz5l4cKFbN22jbCvXylcvAQmVWuQK28+BKXA+39f8uy+LxFhYVSsWInhw4dha2tLtmzZtG26RCYnMDCQhQsXsmnzZkK+fKFgkaKYVK1JngIFEJQCH9/8y7P79wgLDcXEpCx2draMGDGCHDkSasRkBqRgIB0JDg7m9OnTeHl54eNzj9DQUAwNDSlduhTm5uY0bNiQevXqSQcFJXSOkJAQzpw5g5eXF97ed/ny5QsGBgaULFkCc3NzrKyssLa2lnxXQucICwsTffeOtzfBQcEYGBhQrFhRzM3NqV+/Po0aNcLAwEDbpmoVKRiQkJCQkJDI5EjZBBISEhISEpkcKRiQkJCQkJDI5EjBgISEhISERCZHCgYkJCQkJCQyOVIwICEhISEhkcmRggEJCQkJCYlMjhQMSEhISEhIZHKkYEBCQkJCQiKTIwUDEhISEhISmRwpGJCQkJCQkMjkSMGAhISEhIREJkcKBiQkJCQkJDI5UjAgISEhISGRyZGCAQkJCQkJiUyOFAxISEhISEhkcv4HKhqHW+JhenQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 可视化\n",
    "visual_style = {\n",
    "    \"vertex_color\": \"lightblue\",\n",
    "    \"vertex_label\": [0, 1, 2, 3, 4],\n",
    "    \"vertex_size\": 0.4,\n",
    "}\n",
    "\n",
    "fig, axs = plt.subplots(1, 3)\n",
    "ig.plot(\n",
    "    g1,\n",
    "    layout=g1.layout(\"circle\"),\n",
    "    target=axs[0],\n",
    "    **visual_style,\n",
    ")\n",
    "ig.plot(\n",
    "    g2,\n",
    "    layout=g1.layout(\"circle\"),\n",
    "    target=axs[1],\n",
    "    **visual_style,\n",
    ")\n",
    "ig.plot(\n",
    "    g3,\n",
    "    layout=g1.layout(\"circle\"),\n",
    "    target=axs[2],\n",
    "    **visual_style,\n",
    ")\n",
    "fig.text(0.38, 0.5, '$\\simeq$' if g1.isomorphic(g2) else '$\\\\neq$', fontsize=15, ha='center', va='center')\n",
    "fig.text(0.65, 0.5, '$\\simeq$' if g2.isomorphic(g3) else '$\\\\neq$', fontsize=15, ha='center', va='center')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.6 ('py310')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "49ec5068d4d6d3736c39d3918a16f1ca551a23384109b69898c01c2015d1370c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
